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diff --git a/set-theory.html.markdown b/set-theory.html.markdown index 6fb657ed..c6e72960 100644 --- a/set-theory.html.markdown +++ b/set-theory.html.markdown @@ -41,10 +41,10 @@ The cardinality, or size, of a set is determined by the number of items in the s For example, if `S = { 1, 2, 4 }`, then `|S| = 3`. ### The Empty Set -* The empty set can be constructed in set builder notation using impossible conditions, e.g. `∅ = { x : x =/= x }`, or `∅ = { x : x ∈ N, x < 0 }`; +* The empty set can be constructed in set builder notation using impossible conditions, e.g. `∅ = { x : x ≠ x }`, or `∅ = { x : x ∈ N, x < 0 }`; * the empty set is always unique (i.e. there is one and only one empty set); * the empty set is a subset of all sets; -* the cardinality of the empty set is 1, i.e. `|∅| = 1`. +* the cardinality of the empty set is 0, i.e. `|∅| = 0`. ## Representing sets @@ -82,12 +82,12 @@ D = { 2x : x ∈ N } = { 0, 2, 4, 6, 8, ... } * If two sets contain the same items then we say the sets are equal, e.g. `A = B`. * Order does not matter when determining set equality, e.g. `{ 1, 2, 3, 4 } = { 2, 3, 1, 4 }`. * Sets are disjoint, meaning elements cannot be repeated, e.g. `{ 1, 2, 2, 3, 4, 3, 4, 2 } = { 1, 2, 3, 4 }`. -* Two sets `A` and `B` are equal if and only if `A ⊂ B` and `B ⊂ A`. +* Two sets `A` and `B` are equal if and only if `A ⊆ B` and `B ⊆ A`. ## Special Sets ### The Power Set -* Let `A` be any set. The set that contains all possible subsets of `A` is called a "power set" and is written as `P(A)`. If the set `A` contains `n` elements, then `P(A)` contains `2^N` elements. +* Let `A` be any set. The set that contains all possible subsets of `A` is called a "power set" and is written as `P(A)`. If the set `A` contains `n` elements, then `P(A)` contains `2^n` elements. ``` P(A) = { x : x ⊆ A } |